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How to use it?
- Derivative of:
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Derivative of tan(x/2)
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Derivative of (x^2)
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Derivative of sin(x)/2
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Derivative of lnx
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Identical expressions
- acos(tan(x)- zero . one)
- arc co sinus of e of ine of ( tangent of (x) minus 0.1)
- arc co sinus of e of ine of ( tangent of (x) minus zero . one)
- acostanx-0.1
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Similar expressions
- acos(tan(x)+0.1)
- arccos(tan(x)-0.1)
Derivative of acos(tan(x)-0.1)
The solution
You have entered
[src]
acos(tan(x) - 1/10)
$$\operatorname{acos}{\left(\tan{\left(x \right)} - \frac{1}{10} \right)}$$
acos(tan(x) - 1/10)
The first derivative
[src]
/ 2 \
-\1 + tan (x)/
-------------------------
______________________
/ 2
\/ 1 - (tan(x) - 1/10)
$$- \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{1 - \left(\tan{\left(x \right)} - \frac{1}{10}\right)^{2}}}$$
The second derivative
[src]
/ / 2 \ \
/ 2 \ | \1 + tan (x)/*(-1 + 10*tan(x))|
-\1 + tan (x)/*|2*tan(x) + ------------------------------|
| / 2\ |
| | (-1 + 10*tan(x)) | |
| 10*|1 - -----------------| |
\ \ 100 / /
-----------------------------------------------------------
_______________________
/ 2
/ (-1 + 10*tan(x))
/ 1 - -----------------
\/ 100
$$- \frac{\left(2 \tan{\left(x \right)} + \frac{\left(10 \tan{\left(x \right)} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{10 \left(1 - \frac{\left(10 \tan{\left(x \right)} - 1\right)^{2}}{100}\right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{1 - \frac{\left(10 \tan{\left(x \right)} - 1\right)^{2}}{100}}}$$
The third derivative
[src]
/ 2 2 \
| / 2 \ / 2 \ 2 / 2 \ |
/ 2 \ | 2 \1 + tan (x)/ 3*\1 + tan (x)/ *(-1 + 10*tan(x)) 3*\1 + tan (x)/*(-1 + 10*tan(x))*tan(x)|
-\1 + tan (x)/*|2 + 6*tan (x) + --------------------- + ---------------------------------- + ---------------------------------------|
| 2 2 / 2\ |
| (-1 + 10*tan(x)) / 2\ | (-1 + 10*tan(x)) | |
| 1 - ----------------- | (-1 + 10*tan(x)) | 5*|1 - -----------------| |
| 100 100*|1 - -----------------| \ 100 / |
\ \ 100 / /
--------------------------------------------------------------------------------------------------------------------------------------
_______________________
/ 2
/ (-1 + 10*tan(x))
/ 1 - -----------------
\/ 100
$$- \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(6 \tan^{2}{\left(x \right)} + 2 + \frac{3 \left(10 \tan{\left(x \right)} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{5 \left(1 - \frac{\left(10 \tan{\left(x \right)} - 1\right)^{2}}{100}\right)} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{1 - \frac{\left(10 \tan{\left(x \right)} - 1\right)^{2}}{100}} + \frac{3 \left(10 \tan{\left(x \right)} - 1\right)^{2} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{100 \left(1 - \frac{\left(10 \tan{\left(x \right)} - 1\right)^{2}}{100}\right)^{2}}\right)}{\sqrt{1 - \frac{\left(10 \tan{\left(x \right)} - 1\right)^{2}}{100}}}$$